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Journal of Evolution Equations

, Volume 18, Issue 4, pp 1575–1593 | Cite as

Higher-dimensional moving singularities in a superlinear parabolic equation

  • Khin Phyu Phyu Htoo
  • Jin Takahashi
  • Eiji Yanagida
Article

Abstract

This paper is concerned with the existence of singular solutions of a superlinear parabolic equation. It is shown that under some growth conditions on the nonlinearity, there exists a solution whose singularity forms a one or higher-dimensional time-dependent set. Such solutions are constructed by modifying singular solutions of the linear heat equation.

Mathematics Subject Classification

35K58 35A01 35A20 35B33 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Khin Phyu Phyu Htoo
    • 1
  • Jin Takahashi
    • 2
  • Eiji Yanagida
    • 3
  1. 1.Department of MathematicsMandalay UniversityMandalayMyanmar
  2. 2.Department of Mathematical and Computing ScienceTokyo Institute of TechnologyTokyoJapan
  3. 3.Department of MathematicsTokyo Institute of TechnologyTokyoJapan

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